I think you are seriously underestimating the complexity of this endeavour. I suspect it would be easier to clean the North Pacific Gyre with a tea strainer.

Try catching a leaf falling of a tree in autumn some time. Thousands of leaves falling, everywhere, all the time. And yet, you are never in the right place at the right time.

One could probably sail to the middle of the Gyre, toss a bucket over the side and haul it back up, and find nothing but... water. You might see lots of trash float by, lots and lots and lots, but never grab a single piece.

And it is the same with space. Sure, we are led to believe that near space is full of all sorts of shrapnel ready to drill holes through delicate equipment like space shuttles or, heaven forfend, people. Go up there for a week, and you'll wind up shredded like character in a Tex Avery cartoon.

I think people forget how utterly vast space is, even low earth orbit. You are simply not going to rendez-vous with so much as a 2 inch bolt.

I also think you underestimate the mass the reflector would need to be of any use. Unless it was solid metal several centimetres thick, anything colliding with it would just drill right through. If you have sufficient mass to make it useful, you won't have the energy available to move it around. Make it light enough to move around, and you won't be able to do anything, it will just be shredded like a hand going through a rice-paper screen.

God, I sound like a hippy but still, I say we should avail ourselves to cleaning up the oceans. The heavens can wait.

Ada Lovelace for the palindrome
Albert Einstein for having smelly feet
Alfred Nobel for his contribution to battlefield science
Burkhard Heim for providing the missing link between science and mysticism
Claude Shannnon for riding a unicycle at night at MIT
Donald Knuth for being such a great organist
Edward Teller for being the template for Dr. Strangelove
Edwin Hubble for pretending to be a pipe-smoking English gentleman
Erwin Schrödinger for cruelty to cats
Hedy Lamarr for weaponizing pianos
Hugh Everett for immortality, especially for cats
Isaac Newton for his occult studies
Kikunae Ikeda for discovering the secrets of soy sauce
Larry Wall for his website
Louis Camille Maillard for discovering why steaks taste good
Marie Curie for the shiny stuff
Nikola Tesla for the cool cars
Paul Dirac for speaking one word per hour when socializing
Richard Feynman for his bongo skills
Robert Oppenheimer for his in-depth knowledge of the Bhagavad Gita
Rusi P Taleyarkhan for Cold Fusion
Sigmund Freud for his Ménage ā trois
Theodor W Adorno for his contribution to the reception of jazz
Wilhelm Röntgen for the foundations of body scanners
Yulii Borisovich Khariton for the Tsar Bomba
Other (please explain why)